Fractional boundary for the Gott-Hiscock string

A fractional boundary condition is used to join the Gott-Hiscock string to a Levi-Civita vacuum. The use of a fractional derivative generates Israel boundary layers whose density depends on the order of the fractional derivative. Variable boundary layers for the same two bounding space–times can be studied. The string angular deficit depends on the order of the fractional deficit.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87748/2/042506_1.pd

Fractional Boundaries for Fluid Spheres

A single Israel layer can be created when two metrics adjoin with no continuous metric derivative across the boundary. The properties of the layer depend only on the two metrics it separates. By using a fractional derivative match, a family of Israel layers can be created between the same two metrics. The family is indexed by the order of the fractional derivative. The method is applied to Tolman IV and V interiors and a Schwarzschild vacuum exterior. The method creates new ranges of modeling parameters for fluid spheres. A thin shell analysis clarifies pressure/tension in the family of boundary layers.Comment: to appear in J. Math. Phy

Counter-rotating Kerr manifolds separated by a fluid shell

We describe a spheroidal fluid shell between two Kerr vacuum regions which have opposite rotation parameters. The shell has a stiff equation of state and a heat flow vector related to the rotational Killing current. The shell description is useful in exploring the significance of counter-rotation in Kerr metric matches.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65107/2/cqg9_17_175010.pd

Minimal coupling of electromagnetic fields in Riemann–Cartan space‐times for perfect fluids with spin density

The electromagnetic field is minimally coupled to gravity in a Riemann–Cartan space‐time containing a charged magnetized spinning fluid. It is required that the overall Lagrangian of the gravitational field, spinning matter, and the electromagnetic field be invariant under a gauge transformation of the vector potential. The theory preserves both charge conservation and particle number conservation. The electromagnetic field, via the vector potential, now interacts directly with the spin energy momentum. The spin transport equation, in addition to the usual Fermi–Walker transport term, contains a contribution due to the torque of the electromagnetic field acting on a magnetic dipole. In the absence of electromagnetism, the field equations reduce to those of the usual self‐consistent Lagrangian formalism for a perfect fluid with spin density.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71126/2/JMAPAQ-33-3-1073-1.pd

Cosmic string in the van Stockum cylinder

The low density van Stockum dust solution is extended by including an angular deficit factor. The resulting model describes a rotating Gott–Hiscock string surrounded by an annular dust atmosphere. The interior spacetime can be joined to a vacuum Levi-Civita solution with angular deficit.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49211/2/q30901.pd

Raychaudhuri equation in the self-consistent Einstein-Cartan theory with spin-density

The physical implications of the Raychaudhuri equation for a spinning fluid in a Riemann-Cartan spacetime is developed and discussed using the self-consistent Lagrangian based formulation for the Einstein-Cartan theory. It was found that the spin-squared terms contribute to expansion (inflation) at early times and may lead to a bounce in the final collapse. The relationship between the fluid's vorticity and spin angular velocity is clarified and the effect of the interaction terms between the spin angular velocity and the spin in the Raychaudhuri equation investigated. These results should prove useful for studies of systems with an intrinsic spin angular momentum in extreme astrophysical or cosmological problems

The Casimir energy of the twisted string loop: Uniform and two segment loops

We calculate the Casimir energy of a two segment loop of string with one normal boundary point and one twisted boundary point. The energy is renormalized relative to the twisted uniform loop. The use of the twisted loop in simplifying untwisted loop calculations is discussed. © 1996 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70787/2/JMAPAQ-37-8-3662-1.pd

Spin fluid spacetimes from static general relativistic solutions

A method for generating spin fluid solutions to the field equations in a Riemann-Cartan spacetime is presented. The method uses any general relativistic static perfect fluid solution as input. The resulting RC solutions are irrotational and stationary. They will support a nonzero spin density. The spin density has zero Fermi derivative and will not contribute to a circulation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49193/2/cq930516.pd

Spinning fluid cosmologies in Einstein-Cartan theory

We consider self-consistent spinning fluid cosmologies in both general relativity in Riemannian spacetimes and Einstein-Cartan theory in Riemann-Cartan spacetimes. First we extend slightly the cosmological calculation of Martin et al for general relativistic self-consistent spinning fluids. The existence of spin-squared terms in the field equations in the Einstein-Cartan theory shows, however, that an expanded class of meaningful cosmologies is possible. Under certain assumptions on the arbitrariness of the cosmological shear and expansion the results for the ad hoc Weyssenhoff spin fluid in a spherically symmetric spacetime can be reproduced.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49195/2/cq940917.pd

On spherically symmetric cosmology in Riemann-Cartan spacetime with spin-density

We develop the average effective energy-momentum tensor for a spherically symmetric cosmology with randomly oriented spin using the improved energy-momentum tensor in the framework of the self-consistent Einstein-Cartan theory with spin-density.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49194/2/cq941011.pd